Part I: Fill in the Blanks
Solution: Ampere-meter squared ($\text{A m}^2$ or $\text{J/T}$).
Solution: South, North. (Forming continuous closed loops).
Solution: $-\vec{m} \cdot \vec{B}$ (or $-mB \cos\theta$).
Part II: Multiple Choice Questions (MCQs)
Solution: (b) $\vec{m} \times \vec{B}$
Solution: (a) $0^\circ$ (Minimum potential energy, $U = -mB$).
Solution: (c) Never intersect (Otherwise there would be two directions of magnetic field at the point of intersection).
Solution: (c) Bar magnet (Produces identical exterior magnetic field lines).
Solution: (b) Vector quantity (Directed from South to North pole).
Part III: True or False
Solution: True (Magnetic length $\approx$ $5/6$ of geometric length because poles reside slightly inside).
Solution: True ($W = \int_{\theta_1}^{\theta_2} mB\sin\theta d\theta$).
Part IV: Match the Following
Solution:
(P) Torque ($\tau$) $\rightarrow$ (2) $mB\sin\theta$
(Q) Potential Energy ($U$) $\rightarrow$ (3) $-mB\cos\theta$
(R) Magnetic Moment of coil $\rightarrow$ (1) $NIA$
Part I: Fill in the Blanks
Part II: Multiple Choice Questions (MCQs)
Solution: (a) They form continuous closed loops.
Solution: (c) $\oint \vec{B} \cdot d\vec{S} = 0$ (Net flux out of any volume is zero).
Solution: (b) Two smaller, complete dipoles.
Part III: True or False
Solution: False (It is strictly zero).
Part I: Fill in the Blanks
Solution: Dip (or Inclination).
Solution: $0^\circ$ (Zero).
Solution: $B \cos I$ (where $I$ is angle of dip).
Part II: Multiple Choice Questions (MCQs)
Solution: (b) $B^2 = B_H^2 + B_V^2$ (Pythagoras theorem).
Solution: (c) $45^\circ$ ($\tan I = B_V / B_H = 1$).
Solution: (c) Magnetic poles (Field is purely vertical).
Solution: (a) $10^{-4} \text{ Tesla}$ (1 Gauss).
Part III: True or False
Solution: False (It varies from place to place).
Solution: False (It points to the magnetic north pole, which is offset from the geographic north).
Part IV: Match the Following
Solution:
(P) Angle of Dip at Magnetic Equator $\rightarrow$ (2) $0^\circ$
(Q) Angle of Dip at Magnetic Poles $\rightarrow$ (3) $90^\circ$
(R) Ratio of $B_V / B_H$ $\rightarrow$ (1) $\tan I$
Part I: Fill in the Blanks
Solution: Very large ($\mu_r \gg 1$).
Part II: Multiple Choice Questions (MCQs)
Solution: (c) Small and positive.
Solution: (c) $\mu_r > 1$ (slightly).
Part III: True or False
Solution: True (Though it may be masked by stronger paramagnetic or ferromagnetic effects).
Solution: False (It is *inversely* proportional to absolute temperature).
Part IV: Match the Following
Solution:
(P) Diamagnetic $\rightarrow$ (2) Small negative ($-1 < \chi < 0$)
(Q) Paramagnetic $\rightarrow$ (3) Small positive ($\chi > 0$)
(R) Ferromagnetic $\rightarrow$ (1) Large positive ($\chi \gg 1$)
Part I: Fill in the Blanks
Solution: Low (So they demagnetize quickly when current is turned off).
Solution: High (So they are not easily demagnetized by stray fields).
Part II: Multiple Choice Questions (MCQs)
Solution: (c) High permeability, low hysteresis loss.
Solution: (c) Energy dissipated per cycle per unit volume.
Solution: (b) High coercivity (Harder to demagnetize).
Solution: (b) Making transformer cores (To minimize AC heating/energy loss).
Solution: (c) It becomes paramagnetic.
Part III: True or False
Solution: True (High coercivity means it is difficult to demagnetize).
Solution: True (This is called Hysteresis Loss).